Main Points
In reality, entities such as populations tend to interact with others other thna themselves. An analysis of this situation would require two differential equations. Exampels are the Predator-Prey model and the Symbosis model. In the former model, Lotka-Volterra equations are used. In this model, in the absense of predators the prey's population increases and in the absense of prey the predators' population decreases. Multiple population functions can be plotted as a function of time and this information is gotten from the shape of the trajectories of the equations.
Challenges
Is this concept is like those before only with a simultaneous equation twist to it? I do not know how to interprete the slope field or the trajectories. I do not know how the trajectories are obtained . . .
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